Controllable and observable canonical form

Question

M. M. Farhad 2017-2-21

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/326092-controllable-and-observable-canonical-form

评论： Star Strider 2022-6-12

Hi, I want to convert a transfer function to controllable and observable canonical form. Tried with tf2ss but it did not work. I am sharing a part of my code. Is there any way to get those A,B,C,D matrices by any Matlab functions??

My code:

clc; clear all;

Den=[0 1 1]; Num=[1 5 6];

s=tf(Den,Num)

[A B C D]=tf2ss(s)

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Star Strider 2017-2-21

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/326092-controllable-and-observable-canonical-form#answer_255723

编辑：Star Strider 2017-2-21

在 MATLAB Online 中打开

The tf2ss function wants a transfer function as input, not a system object.

Try this:

[A B C D]=tf2ss(Den,Num)
A =
    -5    -6
     1     0
B =
     1
     0
C =
     1     1
D =
     0

EDIT —

To get the state space representation from a system object, just use the ss funciton:

[A B C D] = ss(s);

5 个评论
显示 3更早的评论隐藏 3更早的评论

Star Strider 2017-2-21

在 MATLAB Online 中打开

It does, but not directly. It produces the ‘[A B C D]’ matrices.

You must use the canon function with the 'companion' option to get the controllability canonical form, that it produces by default.

The observability canonical form requires that you transpose the ‘A’ matrix it produces, and then the ‘B’ vector (or matrix) becomes the transposed ‘C’, and the ‘C’ vector (or matrix) becomes the transposed ‘B’.

Example with your system:

Den = [0 1 1];
Num = [1 5 6];
s = tf(Den,Num);
s_ss = ss(s);
s_can_c = canon(s_ss, 'companion');

Controllability —

Amtx_c = s_can_c.A
Bmtx_c = s_can_c.B
Cmtx_c = s_can_c.C
Amtx_c =
     0    -6
     1    -5
Bmtx_c =
     1
     0
Cmtx_c =
     1    -4

Observability —

Amtx_o = s_can_c.A'
Bmtx_o = s_can_c.C'
Cmtx_o = s_can_c.B'
Amtx_o =
     0     1
    -6    -5
Bmtx_o =
     1
    -4
Cmtx_o =
     1     0

I went back to my textbooks to be certain I got this correct. It would help if MATLAB made these a bit easier to find and interpret in the documentation, but then understanding the Jordan-form and companion matrices are essential to understanding controllability and observability.

I apologise for the delay. Life intrudes.